#ifndef Vec3_h
#define Vec3_h
#include <cmath>
#include <cstdlib>
#include <iostream>

class vec3{
public:
    float e[3];
    
    vec3(){}
    vec3(float e0, float e1, float e2){ e[0] = e0; e[1] = e1; e[2] = e2; }
    inline float x() const { return e[0]; }
    inline float y() const { return e[1]; }
    inline float z() const { return e[2]; }
    inline float r() const { return e[0]; }
    inline float g() const { return e[1]; }
    inline float b() const { return e[2]; }
    
    inline const vec3& operator+() const { return *this; }
    inline vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); }
    inline float operator[](int i) const { return e[i]; }
    inline float& operator[](int i) { return e[i]; }
    
    inline vec3& operator+=(const vec3& v);
    inline vec3& operator-=(const vec3& v);
    inline vec3& operator*=(const vec3& v);
    inline vec3& operator/=(const vec3& v);
    inline vec3& operator*=(const float t);
    inline vec3& operator/=(const float t);
    
    inline float length() const {
        return sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]);
    }
    inline float square_length() const{
        return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
    }
    inline void make_unit_vector();
    
    friend inline std::istream & operator>>(std::istream & is, vec3 & t);
    friend inline std::ostream & operator<<(std::ostream & os, vec3 & t);
    friend inline vec3 operator+(const vec3 &v1, const vec3 &v2);
    friend inline vec3 operator-(const vec3 &v1, const vec3 &v2);
    friend inline vec3 operator*(const vec3 &v1, const vec3 &v2);
    friend inline vec3 operator*(const vec3 &v1, float t);
    friend inline vec3 operator*(float t, const vec3 &v1);
    friend inline vec3 operator/(const vec3 &v1, const vec3 &v2);
    friend inline vec3 operator/(const vec3 &v1, float t);
    
    
};

inline std::istream & operator>>(std::istream & is, vec3 & t){
    is >> t.e[0] >> t.e[1] >> t.e[2];
    return is;
}

inline std::ostream & operator<<(std::ostream & os, vec3 & t){
    os << t.e[0] << " " << t.e[1] << " " << t.e[2];
    return os;
}

inline void vec3::make_unit_vector(){
    float k = 1.0 / (sqrt(e[0]*e[0] + e[1]*e[1] + e[2]*e[2]));
    e[0] *= k; e[1] *= k; e[2] *= k;
}

inline vec3 operator+(const vec3 &v1, const vec3 &v2){
    return vec3(v1.e[0] + v2.e[0], v1.e[1] + v2.e[1], v1.e[2] + v2.e[2]);
}

inline vec3 operator-(const vec3 &v1, const vec3 &v2){
    return vec3(v1.e[0] - v2.e[0], v1.e[1] - v2.e[1], v1.e[2] - v2.e[2]);
}

inline vec3 operator*(const vec3 &v1, const vec3 &v2){
    return vec3(v1.e[0] * v2.e[0], v1.e[1] * v2.e[1], v1.e[2] * v2.e[2]);
}

inline vec3 operator*(const vec3 &v1, float t){
    return vec3(v1.e[0] * t, v1.e[1] * t, v1.e[2] * t);
}

inline vec3 operator*(float t, const vec3 &v1){
    return vec3(v1.e[0] * t, v1.e[1] * t, v1.e[2] * t);
}

inline vec3 operator/(const vec3& v1, const vec3& v2){
    return vec3(v1.e[0] / v2.e[0], v1.e[1] / v2.e[1], v1.e[2] / v2.e[2]);
}

inline vec3 operator/(const vec3& v1, float t){
    return vec3(v1.e[0] / t, v1.e[1] / t, v1.e[2] / t);
}

inline float dot(const vec3 &v1, const vec3 &v2){
    return v1.e[0] * v2.e[0] + v1.e[1] * v2.e[1] + v1.e[2] * v2.e[2];
}

inline vec3 cross(const vec3 &v1, const vec3 &v2){
    return vec3(v1.e[1]*v2.e[2] - v1.e[2]*v2.e[1],
                -(v1.e[0]*v2.e[2] - v1.e[2]*v2.e[0]),
                v1.e[0]*v2.e[1] - v1.e[1]*v2.e[0]);
}

inline vec3& vec3::operator+=(const vec3& v){
    e[0] += v.e[0];
    e[1] += v.e[1];
    e[2] += v.e[2];
    return *this;
}
inline vec3& vec3::operator-=(const vec3& v){
    e[0] -= v.e[0];
    e[1] -= v.e[1];
    e[2] -= v.e[2];
    return *this;
}
inline vec3& vec3::operator*=(const vec3& v){
    e[0] *= v.e[0];
    e[1] *= v.e[1];
    e[2] *= v.e[2];
    return *this;
}
inline vec3& vec3::operator/=(const vec3& v){
    e[0] /= v.e[0];
    e[1] /= v.e[1];
    e[2] /= v.e[2];
    return *this;
}
inline vec3& vec3::operator/=(const float t){
    e[0] /= t;
    e[1] /= t;
    e[2] /= t;
    return *this;
}

inline vec3 unit_vector(vec3 v){
    return v / v.length();
}

#endif
